Exact Synthesis Based on Semi-Tensor Product Circuit Solver

In logic synthesis, Boolean satisfiability (SAT) is widely used as a reasoning engine, especially for exact synthesis. By representing input formulas as logic circuits instead of conjunction normal forms (CNFs) as in off-the-shelf CNF-based SAT solvers, circuit-based SAT solvers enable decoding after solution to be easier. An exact synthesis method based on a semi-tensor product (STP) circuit solver is presented in this paper. As opposed to other SAT-based exact synthesis algorithms, synthesized Boolean functions are encoded into STP canonical forms and can be solved by STP-based circuit SAT solver in our method. It can also obtain all optimal solutions in one pass. In particular, all solutions are expressed as 2-lookup tables (LUTs), rather than homogeneous logic representations. Hence, different costs can be considered when selecting the optimal circuit. In experiments, we demonstrate that our method accelerates the runtime up to 225.6X while reducing timeout instances by up to 88%.